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Neural Computation

January 1, 2004, Vol. 16, No. 1, Pages 197-221
(doi: 10.1162/08997660460734056)
© 2003 Massachusetts Institute of Technology
Linear Response Algorithms for Approximate Inference in Graphical Models
Article PDF (188.47 KB)

Belief propagation (BP) on cyclic graphs is an efficient algorithm for computing approximate marginal probability distributions over single nodes and neighboring nodes in the graph. However, it does not prescribe a way to compute joint distributions over pairs of distant nodes in the graph. In this article, we propose two new algorithms for approximating these pairwise probabilities, based on the linear response theorem. The first is a propagation algorithm that is shown to converge if BP converges to a stable fixed point. The second algorithm is based on matrix inversion. Applying these ideas to gaussian random fields, we derive a propagation algorithm for computing the inverse of a matrix.